Hard-square lattice gas

We have studied the hard-square lattice gas, using corner transfer matrices. In particular, we have obtained the first 24 terms of the high-density series for the order parameterρ2−ρ1. From these we estimate the critical activity to be 3.7962±0.0001. This is in excellent agreement with the earlier work of Gaunt and Fisher. It conflicts with the value 4.0 given by Müller-Hartmann and Zittartz's formula for the critical point of the antiferromagnetic Ising model in a field, so we conclude that this formula, while a good approximation, is not exact.

[1]  L. Onsager.  Crystal statistics. I. A two-dimensional model with an order-disorder transition , 1944 .

[2]  D. S. Gaunt,et al.  Hard‐Sphere Lattice Gases. I. Plane‐Square Lattice , 1965 .

[3]  L. K. Runnels,et al.  Exact Finite Method of Lattice Statistics. I. Square and Triangular Lattice Gases of Hard Molecules , 1966 .

[4]  I. Borosh,et al.  Exact solutions of linear equations with rational coefficients by congruence techniques , 1966 .

[5]  R. Baxter,et al.  Dimers on a Rectangular Lattice , 1968 .

[6]  Estimates of the critical exponent β for the Potts model using a variational approximation , 1976 .

[7]  J. Zittartz,et al.  Interface free energy and transition temperature of the square-lattice Ising antiferromagnet at finite magnetic field , 1977 .

[8]  T. Burkhardt.  Interface free energy and critical line for the ising model with nearest and next-nearest-neighbor interactions , 1978 .

[9]  R. Baxter.  Variational approximations for square lattice models in statistical mechanics , 1978 .

[10]  R. Baxter,et al.  Series expansions from corner transfer matrices: The square lattice Ising model , 1979 .

[11]  F. Y. Wu,et al.  Phase diagram of the antiferromagnetic triangular Ising model with anisotropic interactions , 1979 .

[12]  R. Baxter,et al.  An investigation of the high-field series expansions for the square lattice Ising model , 1980 .

[13]  S. K. Tsang,et al.  Entropy of hard hexagons , 1980 .

[14]  D. W. Wood,et al.  Vertex models for the hard-square and hard-hexagon gases, and critical parameters from the scaling transformation , 1980 .